%Class for CO907.
%__________________________________________
%Author: Jiarui Cao
%Date: 19 Nov 2013
%Purpose: Problem Sheet 2. Q2.5a


close all;
clear all;
clc;
clf;

n=200;
%rng('default');

X=normrnd(0,1,n,1);
Mu=mean(X);
Var=var(X);



hold on

%% compute auto corr through xcorr
c=xcorr(X-Mu,'unbiased');
c=c./c((length(c)+1)/2);
plot(c((length(c)+1)/2:length(c)),'sr');
%figure();


%% compute auto corr by hand
R=zeros(n,1);
for tau=0:(n-1)
    TempSum = 0;
    for t=1:n-tau
        TempSum = TempSum + ((X(t)- Mu)*(X(t+tau)-Mu));
    end
    R(tau+1)=TempSum/((n-tau)*Var);
end
plot(R,'o');
xlabel('x');
ylabel('AutoCorr');